Welcome to Apple Support Communities.
Time Machine is a backup file storage and retrieval system, hence the reason you end up in Finder (file system) when you select a prior date.
I think you'd have a better chance of retrieving a recent chat link directly from iChat, File, Recent Items as shown below.
I'm on iChat 5.0.3 (OS X Snow Leopard 10.6), so your screen might look different, but as I recall the same option exists in the Leopard version. (Full chat names are intentionally obscured for confidentiality, so only E's appear in this screen capture.)